A numbering system for artists' colors.
Version of Saturday 22 March 2014.
Dave Barber's other pages.

Manufacturers of art supplies such as:

offer their products (we introduce the generic term stick from their usual shape) in numerous colors, sometimes a huge variety. This chromatic breadth is important because there is limited ability for an artist to mix colors in these media.

In contrast stand artists' paints, which can be mixed freely to obtain intermediate hues, tints, and shades before they are applied to the ground, which might be paper, canvas, china, wood, et cetera. As a result, paint manufacturers need not offer as great a selection to satisfy artistic needs.

When a set of sticks has dozens or hundreds of colors, a systematic labeling scheme is beneficial in helping an artist find a desired color efficiently; this is particularly important when an artist is ordering materials without seeing them first, as from a printed catalog or a web site where color renditions are variable. However, the usual practice in the industry is that manufacturers use names such as "green blue" or "maroon" which, although descriptive, are not precise; also found are names like "outer space" or "jazzberry jam" which, although imaginative, furnish no clue whatever. In mitigation, some artists' paints have names referring to specific chemicals (such as phthalo blue), which is a very reliable way to indicate a hue.

To remedy the uncertainty, we offer a system of triple-digit symbols derived from the four ink colors used in process color printing. More specifically, we employ cyan, magenta, and yellow (abbreviated CMY), because they are suffient to describe the range of colors of sticks. Note that printers find CMY insufficient, needing to combine black ink with these three colors for practical reasons; among them, colored inks meeting the theoretical standard are not available, and black ink is cheaper than the others. However, that is not a problem with the triple-digit system, as it merely describes colors produced by any expeditious means.

Why three colors and not some other number? It is because nearly all human beings have trichromatic vision, being sensitive to particular wavelengths of red (the complement of cyan), green (the complement of magenta), and blue (the complement of yellow). Red, green, and blue (RGB) are the colors used within the pixels of most electronic full-color displays. Each pigment in the sticks absorbs the wavelengths of some color, and reflects or transmits the wavelengths of the complementary color.

Besides pigment, each stick contains non-coloring ingredients forming the binder or vehicle, which keep a powdered pigment from blowing away, and a liquid pigment from dripping away. Crayons often use paraffin, while sidewalk chalk frequently relies on calcium sulfate. A stick with too much pigment and not enough binder will fall apart; but with too much binder and not enough pigment, colors will be faint.

In a triple-digit symbol, the color of a stick is represented by three single-digit numbers (minimum 0, maximum 8) representing respectively how much cyan pigment, how much magenta pigment, and how much yellow pigment would be required in combination to effect the color. This reads "would be" because the manufacturer is not required to actually use cyan, magenta, and yellow pigments; any combination of any pigments is acceptable. For instance, a red crayon would have approximately equal numbers for magenta and yellow, but the manufacturer is free to use a pure red pigment if available. Dark colors will likely have some black pigment mixed in, for practical reasons like those in printing.

A variation of this system might append a fourth digit to indicate transparency of the substance, but we do not pursue that here. Also not covered are the diameter of the lead, the hardness of the lead, fluorescent colors, metallic effects, and sticks that are of predominantly one color with specks of a contrasting color.

This chart shows 25 of the 729 (9 × 9 × 9) colors in the system:

 000  000  000 
 100  010  001 
 200  020  002 
 300  030  003 
 400  040  004 
 500  050  005 
 600  060  006 
 700  070  007 
 800  080  008 

In each case, color 000 is the same neutral white. Color 800 is the strongest cyan; by that term we mean the most saturated cyan that is practical to produce in the medium. Meanwhile, 080 is the strongest magenta, and 008 the strongest yellow.

Within each column, the tints are intended to be "evenly spaced". For example, color 030 should be "halfway" between 020 and 040. Why the cautionary quote marks? Because the human perception of color is very complicated. It can be affected by the lighting in the room where an image is viewed, the colors of adjoining areas within the image, by suggestions of what the colors ought to be from other cues in an image, and sundry physiological factors. Finally, color perception can vary from person to person.

The binder affects how strong the greatest practical color strength can be. For example, the calcium sulfate binder for sidewalk chalk is white, making high saturation difficult. On the other hand, paraffin in thin layers is nearly transparent, meaning that with crayons high saturation is possible. Any amount of transparency also influences the resultant color if the ground is not white, or if one color is layered on top of another.

Displaying colors on a computer screen introduces uncertainty, because equipment varies considerably; thus the images on this page should not be considered a standard. To illustrate this point, when we were developing these charts, we used HTML color codes that exhibited far-from-equal numerical spacing in order to achieve colors that to us looked evenly spaced on our screen.

While it may be difficult for manufacturers to establish numberings that are scientifically objective, any reasonably wrought subjective numbering system is far better than nothing. A useful level of consistency will certainly be possible within a careful manufacturer's set of sticks in a particular medium.

An open question is whether manufacturers should attempt to have numbering consistency between media. Consider a case where the strongest yellow possible in a sidewalk chalk is about the same as the same manufacturer's 004 crayon. Is it better to label the chalk as 008 because it is the strongest in the medium, or is it better to label the chalk as 004, because that puts it on the same scale as crayons?

Few manufacturers will go so far as to produce 729 colors. However, a subset with 125 (5 × 5 × 5) colors, labeled using only the digits 0, 2, 4, 6, and 8, is certainly feasible: sets of pencils with over 100 colors are been sold commercially for years. This table shows the 125 colors:

 000   002   004   006   008 
 020   022   024   026   028 
 040   042   044   046   048 
 060   062   064   066   068 
 080   082   084   086   088 
 200   202   204   206   208 
 220   222   224   226   228 
 240   242   244   246   248 
 260   262   264   266   268 
 280   282   284   286   288 
 400   402   404   406   408 
 420   422   424   426   428 
 440   442   444   446   448 
 460   462   464   466   468 
 480   482   484   486   488 
 600   602   604   606   608 
 620   622   624   626   628 
 640   642   644   646   648 
 660   662   664   666   668 
 680   682   684   686   688 
 800   802   804   806   808 
 820   822   824   826   828 
 840   842   844   846   848 
 860   862   864   866   868 
 880   882   884   886   888 

A separate page shows these same colors arranged in this and other sequences to make comparisons clearer. More detailed is another page which shows all 729 colors.

Use of the system is simple enough. If an artist has pencils numbered 412 and 630 at hand, and desires a color somewhere between them, a likely choice would be pencil number 521:

Sometimes the calculation of halfway incurs a fraction, in which case the artist selects a nearby whole number. If that whole-number color is not available, the artist will have to make do with some approximation. No manufacturer has ever made sticks in all possible colors, but this numbering system does at least enable the artist to systematically determine what colors are candidates for substitution.

Should there eventually be developed a precise, objective method of measuring stick colors, an alternate notation such as 25/56/38 could be adopted, where the 25 indicates the strength of cyan (00 = none, 99 = maximum), 56 of magenta, and 38 of yellow.

The feasibility of an approximate, even if not rigorous, grading scale such as that proposed here is illustrated by the designations used with the graphite pencils long used for artistic and engineering drawing. The hardness of the pencil leads (which, incidentally, do not contain the mineral lead) is denoted on a scale such as the following, with the expected minor variations from one manufacturer to the next:

9B 8B 7B 6B 5B 4B 3B 2B B HB F H 2H 3H 4H 5H 6H 7H 8H 9H
soft medium-soft medium medium-hard hard

Generally, artists prefer the softer grades, because they result in darker lines. On the other hand, engineers prefer the harder grades because they make fine lines easier to draw. Customary is that the harder grades are furnished in smaller diameters than the softer; the same is seen with colored pencils, but those are infrequently graded for either hardness or diameter.

Besides graphite, the principal ingredient of pencil lead is clay; more clay yields a harder material and a lighter line. For instance, a hard lead might be 50% graphite, 45% clay and 5% wax; a soft lead might be 85% graphite, 10% clay and 5% wax.

M.C. Sousa and J.W. Buchanan have prepared an often-quoted table with specific proportions of ingredients for each grade (Computer Graphics Forum, Volume 19, Issue 1, pages 27-49, March 2000). However, those authors make no claim that the numbers are based on laboratory measurements of actual pencil leads; rather their "pencil model" is simply part of a larger scheme they have constructed to simulate, using computer graphics, the look of traditional pencil-on-paper drawing.

A somewhat related topic is here.